2Checkout's system right now doesn't support a direct server-to- server API call for authorizing a credit card, that JS library client-side for the tokenization is required for a transaction.
Would there be a way you could use 2Checkout's Standard checkout instead, grab the sale information from shopify, add the recurring as necessary, then redirect them to 2Checkout? Similar to the existing shopify-2Checkout integration, but with that additional step in between. Not an ideal solution, but if you aren't able to edit the shopify checkout page, might be worth looking into.